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We introduce a class of one-dimensional lattice models in which a quantity, that may be thought of as an energy, is either transported from one site to a neighbouring one, or locally dissipated. Transport is controlled by a continuous bias parameter q, which allows us to study symmetric as well as asymmetric cases. We derive sufficient conditions for the factorization of the N-body stationary distribution and give an explicit solution for the latter, before briefly discussing physically...

Source: http://arxiv.org/abs/cond-mat/0509723v2

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In this short report, I briefly review, illustrate and discuss various techniques (e.g., X ray halos, lensing, kinematics) used to derive mass (hence M/L) profiles of individual galaxies.

Source: http://arxiv.org/abs/astro-ph/0610833v2

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If the X(3872) is a loosely-bound D^{*0} Dbar^0 / D^0 Dbar^{*0} molecule, its inclusive production rate can be described by the NRQCD factorization formalism that applies to inclusive quarkonium production. We argue that if the molecule has quantum numbers J^{PC} = 1^{++}, the most important term in the factorization formula should be the color-octet ^3S_1 term. This is also one of the two most important terms in the factorization formulas for chi_{cJ}. Since the color-octet ^3S_1 term...

Source: http://arxiv.org/abs/hep-ph/0408230v2

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In his approach to analytic number theory C. Deninger has suggested that to the Riemann zeta function $\hat{\zeta}(s)$ (resp. the zeta function $\zeta_Y(s)$ of a smooth projective curve $Y$ over a finite field $\mathbb{F}_q$, $q=p^f$)) one could possibly associate a foliated Riemannian laminated space $(S_{\mathbb{Q}}, \mathcal{F}, g, \phi^t)$ (resp. $(S_Y, \mathcal{F}, g, \phi^t)$) endowed with an action of a flow $\phi^t$ whose primitive compact orbits should correspond to the primes of...

Source: http://arxiv.org/abs/math/0603576v2

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In this article an interpretation and a proof of some classical \\theorems in analysis on the integration of analytic vectors fields are derived from the algebraic method of realization of bialgebras which are constructed with the data of a linear application from a coalgebra into the algebra of right (or left) invariant operators on an approximated coalgebra. The results are obtained from these general algebraic construction and theorems by introducing the more restrictive notion of induced...

Source: http://arxiv.org/abs/math/0607713v1

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It has been suggested that the fuzzy nature of spacetime at the Planck scale may cause lightwaves to lose phase coherence, and if severe enough this could blur images of distant point-like sources sufficiently that they do not form an Airy pattern at the focal plane of a telescope. Blurring this dramatic has already been observationally ruled out by images from Hubble Space Telescope (HST), but I show that the underlying phenomenon could still be stronger than previously considered. It is...

Source: http://arxiv.org/abs/astro-ph/0610422v1

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We consider weakly damped nonlinear Schr\"odinger equations perturbed by a noise of small amplitude. The small noise is either complex and of additive type or real and of multiplicative type. It is white in time and colored in space. Zero is an asymptotically stable equilibrium point of the deterministic equations. We study the exit from a neighborhood of zero, invariant by the flow of the deterministic equation, in $\xLtwo$ or in $\xHone$. Due to noise, large fluctuations off zero occur....

Source: http://arxiv.org/abs/math/0602350v1

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I very briefly discuss the ages and kinematics of spheroids as well as the black hole relations, via a few recent and illustrative studies, which include results on the downsizing, scaling laws, angular momentum and central massive objects.

Source: http://arxiv.org/abs/astro-ph/0610836v2

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The link between nuclear activity and the host galaxy remains elusive. It seems now clear that the galactic environment is not the key, and that there is no significant apparent difference in terms of the presence of bars/spirals between active and non-active galaxies. Nuclear activity nevertheless requires a small central gas reservoir (10^4-10^7 Msun) which may be only partly consumed during the 10^6-10^7 yr AGN duty cycle. A possible route towards a better understanding of the involved...

Source: http://arxiv.org/abs/astro-ph/0610834v1

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This lecture provides some introduction to perfect fluid dynamics within the framework of general relativity. The presentation is based on the Carter-Lichnerowicz approach. It has the advantage over the more traditional approach of leading very straightforwardly to important conservation laws, such as the relativistic generalizations of Bernoulli's theorem or Kelvin's circulation theorem. It also permits to get easily first integrals of motion which are particularly useful for computing...

Source: http://arxiv.org/abs/gr-qc/0603009v1

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Our main aim in this self-contained article is at the same time to detail the relationships between the resurgence and the hyperasymptotic theories, and to demonstrate how these theories can be used for an implicit resurgent function. For this purpose we consider after Stokes the question of the effective Borel-resummation of an exact Bohr-Sommerfeld-like implicit resurgent function whose values on an explicit semi-lattice provide the zeros of the Airy function. The resurgent structure...

Source: http://arxiv.org/abs/math-ph/0602026v1

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We show that reconstructing a tree from order information on triples is NP-hard. This is in contrast to the case for ultra-metrics and for subtree information on quadruples which are both known to allow polynomial time reconstruction.

Source: http://arxiv.org/abs/math/0603116v1

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Title: On linear extension for interpolating sequences. Author: Eric Amar Abstract: Let A be a uniform algebra on the compact space X and $\sigma $ a probability measure on X. We define the Hardy spaces $H^{p}(\sigma)$ and the $H^{p}(\sigma)$ interpolating sequences S in the p-spectrum ${\mathcal{M}}_{p}$ of $\sigma $. We prove, under some structural hypotheses on $\sigma $ that "Carleson type" conditions on S imply that S is interpolating with a linear extension operator in...

Source: http://arxiv.org/abs/math/0610314v1

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We present a new method to count unrooted maps on the sphere up to orientation-preserving homeomorphisms. The principle, called tree-decomposition, is to deform a map into an arborescent structure whose nodes are occupied by constrained maps. Tree-decomposition turns out to be very efficient and flexible for the enumeration of constrained families of maps. In this article, the method is applied to count unrooted 2-connected maps and, more importantly, to count unrooted 3-connected maps, which...

Source: http://arxiv.org/abs/math/0601123v1

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Graphical condensation is a technique used to prove combinatorial identities among numbers of perfect matchings of plane graphs. Propp and Kuo first applied this technique to prove identities for bipartite graphs. Yan, Yeh, and Zhang later applied graphical condensation to nonbipartite graphs to prove more complex identities. Here we generalize some of the identities of Yan, Yeh, and Zhang. We also describe the latest generalization of graphical condensation in which the number of perfect...

Source: http://arxiv.org/abs/math/0605154v1

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We consider stochastic nonlinear Schrodinger equations driven by an additive noise. The noise is fractional in time with Hurst parameter H in (0,1). It is also colored in space and the space correlation operator is assumed to be nuclear. We study the local well-posedness of the equation. Under adequate assumptions on the initial data, the space correlations of the noise and for some saturated nonlinearities, we prove a sample path large deviations principle and a support result. These results...

Source: http://arxiv.org/abs/math/0609423v1

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I derive analytic scalings for coronagraphic imaging searches for extrasolar planets. I compute the efficiency of detecting planets about any given star, and from this compute dimensionless distribution functions for the detected planets as a function of planet-star distance and distance to the host stars. I find the following for blind planet surveys: (1) the optimum wavelength is between 4000-5000 Angstroms for Earth-like planets and 4200-5800 Angstroms for Jovian planets; (2) between 21-32%...

Source: http://arxiv.org/abs/astro-ph/0610697v1

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We study the $t$-deformation of gaussian von Neumann algebras. They appear as example in the theories of Interacting Fock spaces and conditionally free products. When the number of generators is fixed, it is proved that if $t$ sufficiently close to 1, then these algebras do not depend on $t$. In the same way, the notion of conditionally free von Neumann algebras often coincides with freeness.

Source: http://arxiv.org/abs/math/0601557v1

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Let M=M(n,q) be the average of the orders of the elements in the finite unitary group U(n,q). The asymptotic estimate log(M)=nlog(q)-log(n) +o(log n) is proved.

Source: http://arxiv.org/abs/math/0609052v1

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We consider the infinite sequences $(A\_n)\_{n\in\NN}$ of $2\times2$ matrices with nonnegative entries, where the $A\_n$ are taken in a finite set of matrices. Given a vector $V=\pmatrix{v\_1\cr v\_2}$ with $v\_1,v\_2>0$, we give a necessary and sufficient condition for $\displaystyle{A\_1... A\_nV\over|| A\_1... A\_nV||}$ to converge uniformly. In application we prove that the Bernoulli convolutions related to the numeration in Pisot quadratic bases are weak Gibbs.

Source: http://arxiv.org/abs/math/0607704v1

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I briefly review the ''decohering histories'' or ''consistent histories'' formulation of quantum theory, due to Griffiths, Omnes, and Gell-Mann and Hartle (and the subject of my graduate work with George Sudarshan). I also sift through the many meanings that have been attached to decohering histories, with an emphasis on the most basic one: Decoherence of appropriate histories is needed to establish that quantum mechanics has the correct classical limit. Then I will describe efforts to find...

Source: http://arxiv.org/abs/quant-ph/0611293v2

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The electron Hamiltonian of narrow semiconductor rings with the Rashba and Dresselhaus spin orbit terms is invariant under time-reversal operation followed by a large gauge transformation. We find that all the eigenstates are doubly degenerate when integer or half-integer quantum fluxes thread the quantum ring. The wavefunctions of a degenerate pair are related to each other by the symmetry operation. These results are valid even in the presence of a disorder potential. When the Zeeman term is...

Source: http://arxiv.org/abs/cond-mat/0608347v1

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We study the selfsimilarity and the Gibbs properties of several measures defined on the product space $\Omega\_r:=\{0,1,...,\break r-1\}^{\mathbb N}$. This space can be identified with the interval $[0,1]$ by means of the numeration in base $r$. The last section is devoted to the Bernoulli convolution in base $\beta={1+\sqrt5\over2}$, called the Erd\H os measure, and its analogue in base $-\beta=-{1+\sqrt5\over2}$, that we study by means of a suitable system of numeration.

Source: http://arxiv.org/abs/math/0607705v1

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In our previous paper math.QA/0409261, we defined a deformation of the group algebra of the group of even elements of a Coxeter group W, and showed that it is flat for all values of parameters if and only if all the rank 3 parabolic subgroups of W are infinite. In this paper, we study what happens in the general case. Then the deformation is flat only for some values of parameters, and the set of all such values is called the flatness locus. The main result of the paper is an explicit...

Source: http://arxiv.org/abs/math/0604519v2

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We construct a family of BC_n-symmetric biorthogonal abelian functions generalizing Koornwinder's orthogonal polynomials, and prove a number of their properties, most notably analogues of Macdonald's conjectures. The construction is based on a direct construction for a special case generalizing Okounkov's interpolation polynomials. We show that these interpolation functions satisfy a collection of generalized hypergeometric identities, including new multivariate elliptic analogues of Jackson's...

Source: http://arxiv.org/abs/math/0402113v2

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Time-resolved photoelectron spectra are proposed for the measurement of classical information recorded in the quantum phases of a molecular rotational wave packet. Taking Li2 as a prototypical system, we show that an interference arises from the electron-nuclei entanglement induced by the molecular anisotropy. This phenomenon is used to transfer the information that was stored initially in the nuclear rotational degree of freedom into the electronic degree of freedom.

Source: http://arxiv.org/abs/quant-ph/0606068v3

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The structure of the dark energy equation of state phase plane holds important information on the nature of the physics. We explain the bounds of the freezing and thawing models of scalar field dark energy in terms of the tension between the steepness of the potential vs. the Hubble drag. Additionally, we extend the phase plane structure to modified gravity theories, examine trajectories of models with certain properties, and categorize regions in terms of scalar field hierarchical parameters,...

Source: http://arxiv.org/abs/astro-ph/0601052v2

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We address phylogenetic reconstruction when the data is generated from a mixture distribution. Such topics have gained considerable attention in the biological community with the clear evidence of heterogeneity of mutation rates. In our work, we consider data coming from a mixture of trees which share a common topology, but differ in their edge weights (i.e., branch lengths). We first show the pitfalls of popular methods, including maximum likelihood and Markov chain Monte Carlo algorithms. We...

Source: http://arxiv.org/abs/q-bio/0609038v1

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We investigate decoherence in the quantum kicked rotator (modelling cold atoms in a pulsed optical field) subjected to noise with power-law tail waiting-time distributions of variable exponent (Levy noise). We demonstrate the existence of a regime of nonexponential decoherence where the notion of a decoherence rate is ill-defined. In this regime, dynamical localization is never fully destroyed, indicating that the dynamics of the quantum system never reaches the classical limit. We show that...

Source: http://arxiv.org/abs/quant-ph/0611162v1

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In this paper we consider the Newton polygons of $L$-functions coming from additive exponential sums associated to a polynomial over a finite field $\F_q$. These polygons define a stratification of the space of polynomials of fixed degree. We determine the open stratum: we give the generic Newton polygon for polynomials of degree $d\geq 2$ when the characteristic $p$ is greater than 3d, and the Hasse polynomial, i.e. the equation defining the hypersurface complementary to the open stratum.

Source: http://arxiv.org/abs/math/0603264v1

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We present a broad range of measurements of the angular orientation theta_0(t) of the large-scale circulation (LSC) of turbulent Rayleigh-Benard convection as a function of time. We used two cylindrical samples of different overall sizes, but each with its diameter nearly equal to its height. The fluid was water with a Prandtl number of 4.38. The time series theta_0(t) consisted of meanderings similar to a diffusive process, but in addition contained large and irregular spontaneous...

Source: http://arxiv.org/abs/physics/0603088v1

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We investigate the viscosity driven instability in rotating relativistic stars by means of an iterative approach. We focus on polytropic rotating equilibrium stars and impose an m=2 perturbationin the lapse. We vary both the stiffness of the equation of state and the compactness of the star to study those effects on the value of the threshold. For a uniformly rotating star, the criterion T/W, where T is the rotational kinetic energy and W is the gravitational binding energy, mainly depends on...

Source: http://arxiv.org/abs/astro-ph/0606569v3

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We describe some recent refinements of the techniques of threshold resummation, with emphasis on the usefulness of dimensional regularization when applied to nonabelian exponentiation. Threshold resummation is now under theoretical control for DIS and electroweak annihilation cross sections all the way to the fourth tower of logarithms and up to corrections suppressed by powers of the threshold variable.

Source: http://arxiv.org/abs/hep-ph/0607194v1

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A survey of the experimental, phenomenological, and theoretical status of the new heavy mesons is presented. States discussed are the $B_c$, $h_c$, $\eta_c'$, $D_s(2317)$, $D_s(2460)$, X(3872), X(3940), Y(3940), Z(3930), and Y(4260). Quark models for spectra, strong decays, and hadronic interactions are reviewed and used to interpret the new states. New results for strong decay models, bound state decays, mesonic molecules, properties of the X(3872), and the chiral doublet model are also...

Source: http://arxiv.org/abs/hep-ph/0601110v3

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Recent ultrafast experiments have implicated that intrachain base-stacking rather than base-pairing mediate the fate and transport of photoexcited species in DNA chains. Here use an $SU(2)\otimes SU(2)$ lattice model which incorporates both intrachain and interchain electronic interactions to study the quantum mechanical evolution of an initial excitonic state placed on either the adenosine or thymidine side of a model B DNA poly(dA).poly(dT) duplex. Our calculations indicate that over several...

Source: http://arxiv.org/abs/cond-mat/0606333v2

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We discuss the Luttinger-liquid charge-density-wave and Peierls-insulator Mott-insulator quantum phase transitions in 1D electron-phonon systems.

Source: http://arxiv.org/abs/cond-mat/0510741v2

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The X(3872) seems to be a weakly-bound hadronic molecule whose constituents are two charm mesons. Its binding energy is much smaller than all the other energy scales in QCD. This separation of scales can be exploited through factorization formulas for production and decay rates of the X. In a low-energy effective field theory for the constituents of the X, the factorization formulas can be derived using the operator product expansion. The derivations are carried out explicitly for the simplest...

Source: http://arxiv.org/abs/hep-ph/0606115v1

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We consider the unitary group $\U$ of complex, separable, infinite-dimensional Hilbert space as a discrete group. It is proved that, whenever $\U$ acts by isometries on a metric space, every orbit is bounded. Equivalently, $\U$ is not the union of a countable chain of proper subgroups, and whenever $\E\subseteq \U$ generates $\U$, it does so by words of a fixed finite length.

Source: http://arxiv.org/abs/math/0604250v1

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We show that, for a stationary version of Hammersley's process, with Poisson sources on the positive x-axis and Poisson sinks on the positive y-axis, the variance of the length of a longest weakly North--East path $L(t,t)$ from $(0,0)$ to $(t,t)$ is equal to $2\mathbb {E}(t-X(t))_+$, where $X(t)$ is the location of a second class particle at time $t$. This implies that both $\mathbb {E}(t-X(t))_+$ and the variance of $L(t,t)$ are of order $t^{2/3}$. Proofs are based on the relation between the...

Source: http://arxiv.org/abs/math/0603345v2

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Recent ultrafast experiments have implicated intrachain base-stacking rather than base-pairing as the crucial factor in determining the fate and transport of photoexcited species in DNA chains. An important issue that has emerged concerns whether or not a Frenkel excitons is sufficient one needs charge-transfer states to fully account for the dynamics. In we present an $SU(2)\otimes SU(2)$ lattice model which incorporates both intrachain and interchain electronic interactions to study the...

Source: http://arxiv.org/abs/cond-mat/0610784v1

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We show that generalised extreme value statistics -the statistics of the k-th largest value among a large set of random variables- can be mapped onto a problem of random sums. This allows us to identify classes of non-identical and (generally) correlated random variables with a sum distributed according to one of the three (k-dependent) asymptotic distributions of extreme value statistics, namely the Gumbel, Frechet and Weibull distributions. These classes, as well as the limit distributions,...

Source: http://arxiv.org/abs/cond-mat/0601189v2

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Hostile tidal forces may inhibit the formation of Jovian planets in binaries with semimajor axes of $\la$$50\au$, binaries that might be called ``close'' in this context. As an alternative to in situ planet formation, a binary can acquire a giant planet when one of its original members is replaced in a dynamical interaction with another star that hosts a planet. Simple scaling relations for the structure and evolution of star clusters, coupled with analytic arguments regarding binary-single and...

Source: http://arxiv.org/abs/astro-ph/0606645v2

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The recent discoveries of nearby star clusters and associations within a few hundred pc of the Sun, as well as the order of magnitude difference in the formation rates of the embedded and open cluster populations, suggests that additional poor stellar groups are likely to be found at surprisingly close distances to the Sun. Here I describe a new nearby stellar aggregate found by virtue of the parallel proper motions, similar trigonometric parallaxes, and consistent color-magnitude distribution...

Source: http://arxiv.org/abs/astro-ph/0609064v1

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Recent spectroscopic observations of planetary nebulae (PNe) in several elliptical galaxies have revealed structural and kinematical properties of the outer stellar halo regions. In order to elucidate the origin of the properties of these planetary nebula systems (PNSs), we consider the merger scenario in which an elliptical galaxy is formed by merging of spiral galaxies. Using numerical simulations, we particularly investigate radial profiles of projected PNe number densities, rotational...

Source: http://arxiv.org/abs/astro-ph/0606546v1

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We present the basic principles of exact diagonalization and (dynamical) density-matrix renormalization-group approaches to the calculation of ground state and dynamical properties in electron-phonon systems.

Source: http://arxiv.org/abs/cond-mat/0510637v2

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In the quest for precision cosmology, one must ensure that the cosmology is accurate as well. We discuss figures of merit for determining from observations whether the dark energy is a cosmological constant or dynamical, with special attention to the best determined equation of state value, at the ``pivot'' or decorrelation redshift. We show this is not necessarily the best lever on testing consistency with the cosmological constant, and moreover is subject to bias. The standard parametrization...

Source: http://arxiv.org/abs/astro-ph/0604280v2

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We study a continuous family of norm-preserving isometries of the p-adic unit disk, given as interpolations of a common arithmetic function, the q-analog of the identity, for principal p-adic units q. We show that the fixed point set is trivial except when p=3 and q is a generator of the principal 3-adic units; in that case the isometry given by each q has a unique nontrivial 3-adic fixed point, varying homeomorphically with q.

Source: http://arxiv.org/abs/math/0603387v1

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In this paper we study the ergodicity properties of some adaptive Markov chain Monte Carlo algorithms (MCMC) that have been recently proposed in the literature. We prove that under a set of verifiable conditions, ergodic averages calculated from the output of a so-called adaptive MCMC sampler converge to the required value and can even, under more stringent assumptions, satisfy a central limit theorem. We prove that the conditions required are satisfied for the independent Metropolis--Hastings...

Source: http://arxiv.org/abs/math/0610317v1

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The absence of other viable momentum sources for collimated flows leads to the likelihood that magnetic fields play a fundamental role in jet launch and/or collimation in astrophysical jets. To best understand the physics of jets, it is useful to distinguish between the launch region where the jet is accelerated and the larger scales where the jet propagates as a collimated structure. Observations presently resolve jet propagation, but not the launch region. Simulations typically probe the...

Source: http://arxiv.org/abs/astro-ph/0606677v1

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The geometrical meaning of the Eddington-Finkelstein coordinates of Schwarzschild spacetime is well understood: (i) the advanced-time coordinate v is constant on incoming light cones that converge toward r=0, (ii) the angles theta and phi are constant on the null generators of each light cone, (iii) the radial coordinate r is an affine-parameter distance along each generator, and (iv) r is an areal radius, in the sense that 4 pi r^2 is the area of each two-surface (v,r) = constant. The...

Source: http://arxiv.org/abs/gr-qc/0606094v1

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In the case of a rarefaction fan in a non-stationary Hammersley process, we explicitly calculate the asymptotic behavior of the process as we move out along a ray, and the asymptotic distribution of the angle within the rarefaction fan of a second class particle and a dual second class particle. Furthermore, we consider a stationary Hammersley process and use the previous results to show that trajectories of a second class particle and a dual second class particles touch with probability one,...

Source: http://arxiv.org/abs/math/0605199v1

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Continuing work begun in a previous paper, we study the real dynamics of a family of plane birational maps. This time we consider a parameter range where the real and complex dynamics are different. We show in particular that for one parameter value, the real dynamics are transient even though the map is not integrable.

Source: http://arxiv.org/abs/math/0609113v2

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We report the observations of the clear sky fraction at the Concordia station during winter 2006, and derive from it the duty cycle for astronomical observations. Performance in duty cycle and observation duration promotes Dome C for efficient asteroseismic observations. This performance is analyzed and compared to network observation. For network observations, simulations were run considering the helioseismic network GONG as a reference. Observations with 1 site in Antarctica provide...

Source: http://arxiv.org/abs/astro-ph/0612506v1

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Non-negligible dark energy density at high redshifts would indicate dark energy physics distinct from a cosmological constant or ``reasonable'' canonical scalar fields. Such dark energy can be constrained tightly through investigation of the growth of structure, with limits of \la2% of total energy density at z\gg1 for many models. Intermediate dark energy can have effects distinct from its energy density; the dark ages acceleration can be constrained to last less than 5% of a Hubble e-fold...

Source: http://arxiv.org/abs/astro-ph/0603584v2

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We examine the motion in Schwarzschild spacetime of a point particle endowed with a scalar charge. The particle produces a retarded scalar field which interacts with the particle and influences its motion via the action of a self-force. We exploit the spherical symmetry of the Schwarzschild spacetime and decompose the scalar field in spherical-harmonic modes. Although each mode is bounded at the position of the particle, a mode-sum evaluation of the self-force requires regularization because...

Source: http://arxiv.org/abs/gr-qc/0605077v2

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We present measurements of the large-scale circulation (LSC) of turbulent Rayleigh-Benard convection in water-filled cylindrical samples of heights equal to their diameters. The orientation of the LSC had an irregular time dependence, but revealed a net azimuthal rotation with an average period of about 3 days for Rayleigh numbers R > 10^10. On average there was also a tendency for the LSC to be aligned with upflow to the west and downflow to the east, even after physically rotating the...

Source: http://arxiv.org/abs/physics/0608110v1

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A model for the large-scale circulation (LSC) dynamics of turbulent Rayleigh-Benard convection is presented. It consists of two stochastic ordinary differential equations motivated by the Navier-Stokes equation, one each for the strength and the azimuthal orientation of the LSC. Stochastic forces represent phenomenologically the action of the turbulent fluctuations on the LSC. Without adjustable parameters, the model yields a meandering LSC with occasional rotations, and with more rare...

Source: http://arxiv.org/abs/physics/0612120v1

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In the long wavelength domain, typically for wavelengths lambda > 100 angstroms, the laser fields are usually taken as independent of the spatial coordinate. However, at the gas-solid interface the electron density of the material and the incident laser fields vary sharply on a scale of few angstroms. Instead of solving Maxwell equations, we present here a theoretical model, called Electromagnetic Fields from Electron Density (EMFED), generating a continuous vector potential from...

Source: http://arxiv.org/abs/cond-mat/0605231v1

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Continuing work initiated in an earlier publication [Phys. Rev. D 69, 084007 (2004)], we construct a system of light-cone coordinates based at a geodesic world line of an arbitrary curved spacetime. The construction involves (i) an advanced-time or a retarded-time coordinate that labels past or future light cones centered on the world line, (ii) a radial coordinate that is an affine parameter on the null generators of these light cones, and (iii) angular coordinates that are constant on each...

Source: http://arxiv.org/abs/gr-qc/0606093v1

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In recent work (math/0507514) by Etingof, Henriques, Kamnitzer, and the author, a presentation and explicit basis was given for the rational cohomology of the real locus $\bar{M_{0,n}}(\RR)$ of the moduli space of stable genus 0 curves with $n$ marked points. We determine the graded character of the action of $S_n$ on this space (induced by permutations of the marked points), both in the form of a plethystic formula for the cycle index, and as an explicit product formula for the value of the...

Source: http://arxiv.org/abs/math/0601573v2

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We consider a complete noncompact Riemannian manifold M and give conditions on a compact submanifold K of M so that the outward normal exponential map off of the boundary of K is a diffeomorphism onto M\K. We use this to compactify M and show that pinched negative sectional curvature outside K implies M has a compactification with a well defined H\"older structure independent of K. The H\"older constant depends on the ratio of the curvature pinching. This extends and generalizes a...

Source: http://arxiv.org/abs/math/0601503v1

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Despite great advances in our understanding of the formation of the Solar System, the evolution of the Earth, and the chemical basis for life, we are not much closer than the ancient Greeks to an answer of whether life has arisen and persisted on any other planet. The origin of life as a planetary phenomenon will probably resist successful explanation as long as we lack an early record of its evolution and additional examples. It is widely thought that the geologic record shows that life...

Source: http://arxiv.org/abs/astro-ph/0602008v1

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Break-up and recombination processes for loosely-bound molecules composed of atoms with a large scattering length $a$ necessarily involve interactions that are nonperturbative in the exact 2-body interaction. If these processes involve atoms with relative momenta much larger than $\hbar/|a|$, the leading contributions to their rates can be separated into short-distance factors that are insensitive to $a$ and long-distance factors that are insensitive to the range of the interaction. These...

Source: http://arxiv.org/abs/cond-mat/0501510v2

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Baryon acoustic oscillations, measured through the patterned distribution of galaxies or other baryon tracing objects on very large (100 Mpc) scales, offer a possible geometric probe of cosmological distances. Pluses and minuses in this approach's leverage for understanding dark energy are discussed, as are systematic uncertainties requiring further investigation. Conclusions are that 1) BAO offer promise of a new avenue to distance measurements and further study is warranted, 2) the...

Source: http://arxiv.org/abs/astro-ph/0507308v2

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For the space of functions that can be approximated by linear chirps, we prove a reconstruction theorem by random sampling at arbitrary rates.

Source: http://arxiv.org/abs/math/0611608v1

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The fine-structure lines of singly ([Ne II] 12.8 micron) and doubly ([Ne III] 15.6 micron) ionized neon are among the most prominent features in the mid-infrared spectra of star-forming regions, and have the potential to be a powerful new indicator of the star formation rate in galaxies. Using a sample of star-forming galaxies with measurements of the fine-structure lines available from the literature, we show that the sum of the [Ne II] and [Ne III] luminosities obeys a tight, linear...

Source: http://arxiv.org/abs/astro-ph/0611856v1

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We consider the effective resummation of a Borel sum by its associated factorial series expansion. Our approach provides concrete estimates for the remainder term when truncating this factorial series. We then generalize a theorem of Nevanlinna which gives us the natural framework to extend the factorial series method for Borel-resummable fractional power series expansions.

Source: http://arxiv.org/abs/math/0602237v1

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Particles with short-range interactions and a large scattering length have universal low-energy properties that do not depend on the details of their structure or their interactions at short distances. In the 2-body sector, the universal properties are familiar and depend only on the scattering length a. In the 3-body sector for identical bosons, the universal properties include the existence of a sequence of shallow 3-body bound states called "Efimov states" and log-periodic...

Source: http://arxiv.org/abs/cond-mat/0410417v3

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We give a formula for the complex Monge-Ampere operator applied to the maximum of a finite number of functions.

Source: http://arxiv.org/abs/math/0607609v1

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We derive from Einstein equation an evolution law for the area of a trapping or dynamical horizon. The solutions to this differential equation show a causal behavior. Moreover, in a viscous fluid analogy, the equation can be interpreted as an energy balance law, yielding to a positive bulk viscosity. These two features contrast with the event horizon case, where the non-causal evolution of the area and the negative bulk viscosity require teleological boundary conditions. This reflects the local...

Source: http://arxiv.org/abs/gr-qc/0607050v2

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The term ``dynamo'' means different things to the laboratory fusion plasma and astrophysical plasma communities. To alleviate the resulting confusion and to facilitate interdisciplinary progress, we pinpoint conceptual differences and similarities between laboratory plasma dynamos and astrophysical dynamos. We can divide dynamos into three types: 1. magnetically dominated helical dynamos which sustain a large scale magnetic field against resistive decay and drive the magnetic geometry toward...

Source: http://arxiv.org/abs/astro-ph/0604221v1

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We argue that gravitational instability in the outer parts of collapsar disks may lead to fragmentation near the radius where helium photodisintegrates, because of the strong cooling provided by this process. This physics sets clear physical scales for the fragmentation conditions and the properties of gravitationally bound clumps. Collapse of a fragment proceeds until the neutrons become degenerate; a neutron star of mass ~0.1-1Msun may result. We find that tidal disruption of a fragment and...

Source: http://arxiv.org/abs/astro-ph/0610696v2

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The time-convolutionless master equation for the electronic populations is derived for a generic electron-phonon Hamiltonian. The equation can be used in the regimes where the golden rule approach is not applicable. The equation is applied to study the electronic relaxation in several models with the finite number normal modes. For such mesoscopic systems the relaxation behavior differs substantially from the simple exponential relaxation. In particular, the equation shows the appearance of the...

Source: http://arxiv.org/abs/cond-mat/0606497v1

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It is difficult to imagine a planet formation model that does not at some stage include a gravitationally unstable disc. Initially unstable gas-dust discs may form planets directly, but the high surface density required has motivated the alternative that gravitational instability occurs in a dust sub-layer only after grains have grown large enough by electrostatic sticking. Although such growth up to the instability stage is efficient for laminar discs, concern has mounted as to whether...

Source: http://arxiv.org/abs/astro-ph/0509701v2

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In a transiting planetary system, the presence of a second planet will cause the time interval between transits to vary. These transit timing variations (TTV) are particularly large near mean-motion resonances and can be used to infer the orbital elements of planets with masses that are too small to detect by any other means. I present the results of a study of simulated data where I show the potential that this planet detection technique has to detect and characterize secondary planets in...

Source: http://arxiv.org/abs/astro-ph/0612442v1

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We examine the pattern of star birth in the Orion Nebula Cluster (ONC), with the goal of discerning the cluster's formation mechanism. Outside of the Trapezium, the distribution of stellar masses is remarkably uniform, and is not accurately described by the field-star initial mass function. The deconvolved, three-dimensional density of cluster members peaks at the Trapezium stars, which are truly anomalous in mass. Using theoretical pre-main-sequence tracks, we confirm the earlier finding that...

Source: http://arxiv.org/abs/astro-ph/0603138v1

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It is shown that quark mass dependence induced by one loop corrections to the Breit-Fermi spin-dependent one gluon exchange potential permit an accurate determination of heavy-light meson masses. Thus the $D_s(2317)$ is a canonical $c\bar s$ meson in this scenario. The multiplet splitting relationship of chiral doublet models, $M(1^+)-M(1^-) = M(0^+) -M(0^-)$, holds to good accuracy in the $D$ and $D_s$ systems, but is accidental. Radiative transitions and bottom flavoured meson masses are...

Source: http://arxiv.org/abs/hep-ph/0608011v2

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Active Galactic Nuclei can produce extremely powerful jets. While tightly collimated, the scale of these jets and the stellar density at galactic centers implies that there will be many jet/star interactions, which can mass-load the jet through stellar winds. Previous work employed modest wind mass outflow rates, but this does not apply when mass loading is provided by a small number of high mass-loss stars. We construct a framework for jet mass-loading by stellar winds for a broader spectrum...

Source: http://arxiv.org/abs/astro-ph/0604585v1

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This paper studies the behavior under iteration of the maps T_{ab}(x,y) = (F_{ab}(x)- y, x) of the plane R^2, in which F_{ab}(x)= ax if x>0 and bx if x

Source: http://arxiv.org/abs/math/0505103v3

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For estimating a positive normal mean, Zhang and Woodroofe (2003) as well as Roe and Woodroofe (2000) investigate 100($1-\alpha)%$ HPD credible sets associated with priors obtained as the truncation of noninformative priors onto the restricted parameter space. Namely, they establish the attractive lower bound of $\frac{1-\alpha}{1+\alpha}$ for the frequentist coverage probability of these procedures. In this work, we establish that the lower bound of $\frac{1-\alpha}{1+\alpha}$ is applicable...

Source: http://arxiv.org/abs/math/0611684v1

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We present a combined analysis of all publicly available, visible HST observations of transits of the planet HD 209458b. We derive the times of transit, planet radius, inclination, period, and ephemeris. The transit times are then used to constrain the existence of secondary planets in the system. We show that planets near an Earth mass can be ruled out in low-order mean-motion resonance, while planets less than an Earth mass are ruled out in interior, 2:1 resonance. We also present a combined...

Source: http://arxiv.org/abs/astro-ph/0610159v1

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Atoms with a large scattering length have universal low-energy properties that do not depend on the details of their structure or their interactions at short distances. In the 2-atom sector, the universal properties are familiar and depend only on the scattering length. In the 3-atom sector for identical bosons, the universal properties include the existence of a sequence of shallow triatomic molecules called Efimov trimers and log-periodic dependence of scattering observables on the energy and...

Source: http://arxiv.org/abs/cond-mat/0612123v1

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We study the kinematics of gaseous disks in triaxial dark matter halos using the closed-loop orbit solutions in non-axisymmetric potentials. The orbits are in general non-circular and, for given triaxiality, their ellipticity depends on the ratio of escape to circular velocities, V_esc^2/V_c^2. This ratio increases steeply towards the center for cold dark matter (CDM) halo density profiles, implying that even minor deviations from spherical symmetry may induce large deviations from circular...

Source: http://arxiv.org/abs/astro-ph/0608376v2

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We present an improved coupling technique for analyzing the mixing time of Markov chains. Using our technique, we simplify and extend previous results for sampling colorings and independent sets. Our approach uses properties of the stationary distribution to avoid worst-case configurations which arise in the traditional approach. As an application, we show that for $k/\Delta >1.764$, the Glauber dynamics on $k$-colorings of a graph on $n$ vertices with maximum degree $\Delta$ converges in...

Source: http://arxiv.org/abs/math/0610188v1

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Common gastropods such as snails crawl on a solid substrate by propagating muscular waves of shear stress on a viscoelastic mucus. Producing the mucus accounts for the largest component in the gastropod's energy budget, more than twenty times the amount of mechanical work used in crawling. Using a simple mechanical model, we show that the shear-thinning properties of the mucus favor a decrease in the amount of mucus necessary for crawling, thereby decreasing the overall energetic cost of...

Source: http://arxiv.org/abs/cond-mat/0608363v2

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This paper studies the behavior under iteration of the maps T_{ab}(x,y) = (F_{ab}(x)-y,x) of the plane R^2, in which F_{ab}(x)=ax if x>=0 and bx if x

Source: http://arxiv.org/abs/math/0301294v4

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We present here a brief overview of our work in developing a convolutionless quantum master equation approach suitable for mesoscopic sized systems. Our final equation can be used in the regimes where the golden rule approach is not applicable. Here we apply the approach to study the electronic relaxation in several models with the finite number of normal modes. For such mesoscopic systems the relaxation behavior differs substantially from the simple exponential relaxation. In particular, the...

Source: http://arxiv.org/abs/cond-mat/0610772v1

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We use the Hopf fibrillation to give simple and intuitive geometric constructions of the 24-cell, $E_8$ and $\Lambda_{16}$ lattices.

Source: http://arxiv.org/abs/math/0612728v1

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Theoretical studies predict that Trojans are likely a frequent byproduct of planet formation and evolution. We present a novel method of detecting Trojan companions to transiting extrasolar planets which involves comparing the time of central eclipse with the time of the stellar reflex velocity null. We demonstrate that this method offers the potential to detect terrestrial-mass Trojans using existing ground-based observatories. This method rules out Trojan companions to HD 209458b and HD...

Source: http://arxiv.org/abs/astro-ph/0609298v2

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The galaxy cluster 1E 0657-56 has a bullet-like subcluster that is moving away from the centre of the main cluster at high speed. Markevitch et al. (2004) recently estimated a relative velocity of V_bullet = 4500 +1100/-800 km/s, based on observations of the bow shock in front of the subcluster. The weak lensing analysis of Clowe et al. (2004) indicates that a substantial secondary mass peak is associated with this subcluster. We estimate the likelihood of such a configuration by examining the...

Source: http://arxiv.org/abs/astro-ph/0604443v1

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We determine the structure of the center and the trace space of the centrally extended preprojective algebra of an ADE quiver, introduced by the first and the third authors in math/0503393. It turns out that this structure has a mysterious relationship to the structure of the maximal nilpotent subalgebra of the corresponding simple Lie algebra.

Source: http://arxiv.org/abs/math/0606403v1

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When one expands a Schur function in terms of the irreducible characters of the symplectic (or orthogonal) group, the coefficient of the trivial character is 0 unless the indexing partition has an appropriate form. A number of q-analogues of this fact were conjectured in math.QA/0112035; the present paper proves most of those conjectures, as well as some new identities suggested by the proof technique. The proof involves showing that a nonsymmetric version of the relevant integral is...

Source: http://arxiv.org/abs/math/0606204v1

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We propose that n-type semiconductor quantum dots with the Rashba and Dresselhaus spin orbit interactions may be used for single electron manipulation through adiabatic transformations between degenerate states. All the energy levels are discrete in quantum dots and possess a double degeneracy due to time reversal symmetryin the presence of the Rashba and/or Dresselhaus spin orbit coupling terms. We find that the presence of double degeneracy does not necessarily give rise to a finite...

Source: http://arxiv.org/abs/cond-mat/0602512v1

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Torque fluctuations due to magnetorotational turbulence in proto-planetary disks may greatly influence the migration patterns and survival probabilities of nascent planets. Provided that the turbulence is a stationary stochastic process with finite amplitude and correlation time, the resulting diffusive migration can be described with a Fokker-Planck equation, which we reduce to an advection-diffusion equation. We calibrate the coefficients with existing turbulent-disk simulations and...

Source: http://arxiv.org/abs/astro-ph/0603235v2

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We complete the project begun by Callahan, Dean and Weeks to identify all knots whose complements are in the SnapPea census of hyperbolic manifolds with seven or fewer tetrahedra. Many of these ``simple'' hyperbolic knots have high crossing number. We also compute their Jones polynomials.

Source: http://arxiv.org/abs/math/0311380v4

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We describe a new method for robustly testing theoretical predictions of red giant evolution near the tip of the giant branch. When theoretical cumulative luminosity functions are shifted to align the tip in I-band and normalized at a luminosity level slightly brighter than the red giant bump, virtually all dependence on age and composition (heavy elements and helium abundance) is eliminated. While significant comparisons with observations require large samples of giant stars, such samples are...

Source: http://arxiv.org/abs/astro-ph/0611278v1

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We present a near-optimal reduction from approximately counting the cardinality of a discrete set to approximately sampling elements of the set. An important application of our work is to approximating the partition function $Z$ of a discrete system, such as the Ising model, matchings or colorings of a graph. The typical approach to estimating the partition function $Z(\beta^*)$ at some desired inverse temperature $\beta^*$ is to define a sequence, which we call a {\em cooling schedule},...

Source: http://arxiv.org/abs/cs/0612058v1

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We present here a formulation of the electronic ground-state energy in terms of the second order reduced density matrix, using a duality argument. It is shown that the computation of the ground-state energy reduces to the search of the projection of some two-electron reduced Hamiltonian on the dual cone of $N$-representability conditions. Some numerical results validate the approach, both for equilibrium geometries and for the dissociation curve of N$_2$.

Source: http://arxiv.org/abs/quant-ph/0602042v2

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Integral field spectrographs are major instruments to study the mechanisms involved in the formation and the evolution of early galaxies. When combined with multi-object spectroscopy, those spectrographs can behave as machines used to derive physical parameters of galaxies during their formation process. Up to now, there is only one available spectrograph with multiple integral field units, e.g. FLAMES/GIRAFFE on the VLT. However, current ground based instruments suffer from a degradation of...

Source: http://arxiv.org/abs/astro-ph/0612538v1

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H$_3^+$ emission is the dominant cooling mechanism in Jupiter's thermosphere and a useful probe of temperature and ion densities. The H$_3^+$ ion is predicted to form in the thermospheres of close-in `hot Jupiters' where its emission would be a significant factor in the thermal energy budget, affecting temperature and the rate of hydrogen escape from the exosphere. Hot Jupiters are predicted to have up to 10$^5$ times Jupiter's H$_3^+$ emission because they experience extreme stellar...

Source: http://arxiv.org/abs/astro-ph/0605708v1